Identifier
Mp00017: Binary trees to 312-avoiding permutationPermutations
Mp00061: Permutations to increasing tree Binary trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-2
[.,.]=>[1]=>[.,.] [.,[.,.]]=>[2,1]=>[[.,.],.] [[.,.],.]=>[1,2]=>[.,[.,.]] [.,[.,[.,.]]]=>[3,2,1]=>[[[.,.],.],.] [.,[[.,.],.]]=>[2,3,1]=>[[.,[.,.]],.] [[.,.],[.,.]]=>[1,3,2]=>[.,[[.,.],.]] [[.,[.,.]],.]=>[2,1,3]=>[[.,.],[.,.]] [[[.,.],.],.]=>[1,2,3]=>[.,[.,[.,.]]] [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[[[[.,.],.],.],.] [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[[[.,[.,.]],.],.] [.,[[.,.],[.,.]]]=>[2,4,3,1]=>[[.,[[.,.],.]],.] [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[[[.,.],[.,.]],.] [.,[[[.,.],.],.]]=>[2,3,4,1]=>[[.,[.,[.,.]]],.] [[.,.],[.,[.,.]]]=>[1,4,3,2]=>[.,[[[.,.],.],.]] [[.,.],[[.,.],.]]=>[1,3,4,2]=>[.,[[.,[.,.]],.]] [[.,[.,.]],[.,.]]=>[2,1,4,3]=>[[.,.],[[.,.],.]] [[[.,.],.],[.,.]]=>[1,2,4,3]=>[.,[.,[[.,.],.]]] [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [[.,[[.,.],.]],.]=>[2,3,1,4]=>[[.,[.,.]],[.,.]] [[[.,.],[.,.]],.]=>[1,3,2,4]=>[.,[[.,.],[.,.]]] [[[.,[.,.]],.],.]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [[[[.,.],.],.],.]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.] 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[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]] [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]] [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]] [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]] [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]] [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]] [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]] [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]] [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]] [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]] [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]] [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]] [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]] [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]] [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]] [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]] [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]] [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]] [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]] [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]] [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]] [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]] [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.] [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[[[[[.,[.,.]],.],.],.],.] [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[[[[.,[[.,.],.]],.],.],.] [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[[[[[.,.],[.,.]],.],.],.] [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[[[[.,[.,[.,.]]],.],.],.] [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[[[.,[[[.,.],.],.]],.],.] [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[[[.,[[.,[.,.]],.]],.],.] [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[[[[.,.],[[.,.],.]],.],.] 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[.,[[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],.]]=>[6,5,8,7,9,4,10,3,11,2,12,1]=>[[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],.] [.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]]=>[5,4,8,7,9,6,10,3,11,2,12,1]=>[[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]],.] [.,[[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],.]]=>[6,5,7,4,9,8,10,3,11,2,12,1]=>[[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],.] [.,[[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],.]]=>[5,4,7,6,9,8,10,3,11,2,12,1]=>[[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]],.] [.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]]=>[4,3,8,7,9,6,10,5,11,2,12,1]=>[[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]],.] [.,[[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],.]]=>[4,3,7,6,9,8,10,5,11,2,12,1]=>[[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]],.] [.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,9,8,10,7,11,2,12,1]=>[[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]],.] [.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]]=>[4,3,6,5,9,8,10,7,11,2,12,1]=>[[[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],[.,.]],.] [.,[[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],.]]=>[6,5,7,4,8,3,10,9,11,2,12,1]=>[[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]],.] [.,[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],.]]=>[5,4,7,6,8,3,10,9,11,2,12,1]=>[[[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]],.] [.,[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],.]]=>[4,3,7,6,8,5,10,9,11,2,12,1]=>[[[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]],.] [.,[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],.]]=>[5,4,6,3,8,7,10,9,11,2,12,1]=>[[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]],.] [.,[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],.]]=>[4,3,6,5,8,7,10,9,11,2,12,1]=>[[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]],.] [.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[3,2,8,7,9,6,10,5,11,4,12,1]=>[[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.] [.,[[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[3,2,7,6,9,8,10,5,11,4,12,1]=>[[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]],.] [.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[3,2,6,5,9,8,10,7,11,4,12,1]=>[[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]],.] [.,[[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[3,2,7,6,8,5,10,9,11,4,12,1]=>[[[.,.],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],.] [.,[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[3,2,6,5,8,7,10,9,11,4,12,1]=>[[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]],.] [.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]]=>[4,3,5,2,9,8,10,7,11,6,12,1]=>[[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]],.] [.,[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,5,2,8,7,10,9,11,6,12,1]=>[[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]],.] [.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]]=>[3,2,5,4,9,8,10,7,11,6,12,1]=>[[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]],.] [.,[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],.]]=>[3,2,5,4,8,7,10,9,11,6,12,1]=>[[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]],.] [.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]]=>[5,4,6,3,7,2,10,9,11,8,12,1]=>[[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]],.] [.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]]=>[4,3,6,5,7,2,10,9,11,8,12,1]=>[[[[.,.],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]],.] [.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,10,9,11,8,12,1]=>[[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],.] [.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]]=>[4,3,5,2,7,6,10,9,11,8,12,1]=>[[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]],.] [.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]]=>[3,2,5,4,7,6,10,9,11,8,12,1]=>[[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]],.] [.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]]=>[6,5,7,4,8,3,9,2,11,10,12,1]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]],.] [.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]]=>[5,4,7,6,8,3,9,2,11,10,12,1]=>[[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]],.] [.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]]=>[4,3,7,6,8,5,9,2,11,10,12,1]=>[[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]],.] [.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]]=>[5,4,6,3,8,7,9,2,11,10,12,1]=>[[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],.] [.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]=>[4,3,6,5,8,7,9,2,11,10,12,1]=>[[[[.,.],[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]],.] [.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]]=>[3,2,7,6,8,5,9,4,11,10,12,1]=>[[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.] [.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[3,2,6,5,8,7,9,4,11,10,12,1]=>[[[.,.],[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]],.] [.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,8,7,9,6,11,10,12,1]=>[[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],.] [.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[3,2,5,4,8,7,9,6,11,10,12,1]=>[[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]],.] [.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]]=>[5,4,6,3,7,2,9,8,11,10,12,1]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]],.] [.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]=>[4,3,6,5,7,2,9,8,11,10,12,1]=>[[[[.,.],[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]],.] [.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[3,2,6,5,7,4,9,8,11,10,12,1]=>[[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]],.] [.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]=>[4,3,5,2,7,6,9,8,11,10,12,1]=>[[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]],.] [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,9,8,11,10,12,1]=>[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],.] [[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[2,1,8,7,9,6,10,5,11,4,12,3]=>[[.,.],[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]] 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[[.,[[.,[.,.]],.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[3,2,4,1,8,7,10,9,11,6,12,5]=>[[[.,.],[.,.]],[[[[.,.],[[.,.],[.,.]]],[.,.]],.]] [[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,4,1,7,6,10,9,11,8,12,5]=>[[[.,.],[.,.]],[[[.,.],[[[.,.],[.,.]],[.,.]]],.]] [[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[3,2,4,1,8,7,9,6,11,10,12,5]=>[[[.,.],[.,.]],[[[[.,.],[.,.]],[[.,.],[.,.]]],.]] [[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,4,1,7,6,9,8,11,10,12,5]=>[[[.,.],[.,.]],[[[.,.],[[.,.],[[.,.],[.,.]]]],.]] [[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[2,1,4,3,9,8,10,7,11,6,12,5]=>[[.,.],[[.,.],[[[[[.,.],[.,.]],[.,.]],[.,.]],.]]] [[[.,[.,.]],[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[2,1,4,3,8,7,10,9,11,6,12,5]=>[[.,.],[[.,.],[[[[.,.],[[.,.],[.,.]]],[.,.]],.]]] [[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[2,1,4,3,7,6,10,9,11,8,12,5]=>[[.,.],[[.,.],[[[.,.],[[[.,.],[.,.]],[.,.]]],.]]] 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[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] [[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]] [[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9,10,11]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9,10]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]] [[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]=>[3,4,2,5,1,6,7,8,9]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]] [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] [[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]=>[7,6,5,8,4,3,2,1,9]=>[[[[[[[.,.],.],[.,.]],.],.],.],[.,.]] [[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.]=>[6,7,5,8,4,3,2,1,9]=>[[[[[[.,[.,.]],[.,.]],.],.],.],[.,.]] [[[[[[.,[[.,.],.]],[.,.]],.],.],.],.]=>[2,3,1,5,4,6,7,8,9]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]] [[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]] [[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]]=>[4,3,2,1,6,7,8,9,10,5]=>[[[[.,.],.],.],[[.,[.,[.,[.,[.,.]]]]],.]] [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,3,9,8,7,6,5,4,1]=>[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.] [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[2,8,7,6,5,4,3,1,9]=>[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,7,1,9,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] [[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[1,3,4,2,5,6,7,8,9]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]] [[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[8,7,6,5,4,3,2,9,1,10]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,8,10,9,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] [[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]=>[2,1,3,5,6,7,8,9,4]=>[[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]] [[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.]=>[5,6,4,3,2,1,7,8,9]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]] [[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]=>[5,6,4,3,2,1,7,8,9,10]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]] [[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.]=>[6,7,5,4,3,2,1,8,9,10,11]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,[.,.]]]]] [[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.]=>[6,7,5,4,3,2,1,8,9,10]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,.]]]] [[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.]=>[5,6,4,3,2,7,1,8,9]=>[[[[[.,[.,.]],.],.],[.,.]],[.,[.,.]]] [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[6,7,5,4,3,2,1,8,9]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,.]]] [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[7,6,5,4,3,2,1,9,10,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,[.,.]],.]]
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.